Can you spot the difference between a rhombus and a parallelogram? A regular polygon and an irregular one? In Grade 6, you'll master the properties of all 2D polygons, classify every quadrilateral, identify lines of symmetry and rotational symmetry, and even construct triangles accurately with a ruler and protractor.
š· Quadrilateral Family
Square ā Rectangle ā Rhombus ā Parallelogram ā Trapezium ā Kite (each has fewer properties than the last!)
š A regular polygon has ALL sides equal AND all angles equal. Examples: equilateral triangle, square, regular pentagon, regular hexagon.
š An irregular polygon has sides or angles that are not all equal.
šŖ Lines of symmetry (reflection symmetry): fold the shape ā the two halves must match exactly. A regular polygon with n sides has n lines of symmetry.
š Rotational symmetry order: how many positions a shape looks identical during one full 360Ā° rotation. A shape with no rotational symmetry has order 1.
š· Quadrilaterals are a family: a square is a special rectangle, a rectangle is a special parallelogram. Properties are inherited going "up" the family.
š When constructing triangles: use a ruler for the base, a protractor to measure angles accurately.
A regular polygon has an exterior angle of 45Ā°. How many sides does it have? What is it called?
Explain why a square is a rhombus but a rhombus is not always a square.
A quadrilateral has angles 3xĀ°, 4xĀ°, 5xĀ° and 6xĀ°. Find x and all four angles.
Draw a shape that has exactly 2 lines of symmetry and rotational order 2. Name it.
The sum of interior angles of a polygon is 1,260Ā°. How many sides does it have?
A regular polygon's interior angle is 5 times its exterior angle. Find both angles and the number of sides.
Prove that the angles in any triangle sum to 180Ā° using the property of parallel lines.
A parallelogram has one angle of 65Ā°. Find the other three angles and explain your reasoning.
How many diagonals does a regular hexagon have?
A shape has 4 lines of symmetry and rotational symmetry of order 4. What shapes could it be?
Challenge Answers
360 Ć· 45 = 8 sides ā regular octagon
A square has 4 equal sides (like a rhombus) but also has 4 right angles (which a rhombus doesn't need to have). So a square satisfies all conditions of a rhombus, but a rhombus doesn't always have right angles ā therefore a rhombus is not always a square.
Interior + exterior = 180Ā°. Let exterior = x, interior = 5x. So 5x + x = 180 ā 6x = 180 ā x = 30Ā° (exterior), interior = 150Ā°. Sides = 360 Ć· 30 = 12 sides (dodecagon)
Draw a line parallel to the base through the apex. The alternate angles equal the two base angles of the triangle. All three angles together form a straight line (180Ā°). Therefore angles in a triangle sum to 180Ā°.
Opposite angles are equal ā another angle is also 65Ā°. Adjacent angles are supplementary ā 180Ā° ā 65Ā° = 115Ā°. So the four angles are: 65Ā°, 115Ā°, 65Ā°, 115Ā°.
Using the formula n(nā3) Ć· 2 = 6 Ć 3 Ć· 2 = 9 diagonals
Square ā it is the only quadrilateral with 4 lines of symmetry and rotational order 4. (Any regular polygon with 4 sides where all sides and angles are equal also qualifies ā in the quadrilateral family, only the square meets this criterion.)